32 CLIMATIC CYCLES AND TREE-GROWTH 



over which the absence produces uncertainty. A missing ring here 

 and there can be located with perfect exactness and causes no uncer- 

 tainty of dating. In fact, so many missing rings have been found after 

 careful search that they often increase the feeling of certainty in the 

 dating of rings. 



Missing rings occur when autumn rings merge together in the 

 absence of any spring growth. This rarely, if ever, occurs about the 

 entire circumference of the tree. There are a few cases in which, if 

 the expression may be excused, I have traced a missing ring entirely 

 around a tree without finding it. I have observed many cases in which 

 the missing ring has been evident in less than 10 per cent of the circum- 

 ference. Some are absent in only a small part of their circuit. I have 

 observed change in this respect at different heights in the tree, but 

 have not followed that line of study further. It can be studied in the 

 longitudinally bisected tree. A missing ring is often represented by a 

 slight enlargement of the red autumn ring of the previous year. 



One sees from this discussion what the probable errors may be in 

 mere counting of rings. In the first work on the yellow pines, the 

 dating was done by simple counting. Accurate dating in the same 

 trees (19 of them) later showed that the average error in counting 

 through the last 200 years was 4 per cent, due practically always to 

 missing rings. A comparison in 7 sequoias between very careful 

 counting on the stump and accurate dating in 2,000 years shows an 

 average counting error of 35 years, which is only 1.7 per cent (Volume 

 I, pp. 15 and 45). 



Simulated doubles — In the process of counting and dating rings 

 in Arizona pines, two sharp red rings sometimes occur close together, 

 giving the appearance of a double and leaving one in doubt as to 

 whether one year or two is involved. In such cases the following 

 probabilities apply: If the tree has other obvious doubles, the case 

 in hand is likely but not certain to be another doubling. If the two 

 red rings are unequal in size and the smaller one is inside, that is, 

 nearer the center, it is likely to be a real double formed by the spring 

 drought. If the smaller one is outside the larger, it is probably a 

 separate year. If the two rings are equal and either one shows a 

 further doubling, the two rings in question are separate years. If 

 the case is still doubtful, cross-identification may settle it. But if 

 that fails, the doubtful part should be discarded. The most tantalizing 

 case of this kind that I have is an early historic beam from Pecos, 

 KL-I, in which all kinds of doubles are exhibited. 



Reinforced rings — Certain groups of prehistoric specimens from 

 the Wupatki National Monument, northeast of Flagstaff, show heavy 

 reinforcement in the youth rings of many trees. That consists of 

 very hard tissue formed during the rapid spring growth, so that each 



